when you first started this thread, i googled the phrase, and lots of non-AA stuff comes up from sites related in any way, shape or form to addiction, recovery, racing, rockclimbing.....
when i take it literally, i think it explains the meaning quite well: hanging on to something so tightly, so freaked-outly, so terrified, that ones knuckles turn white.
actually, there seemed to be a few websites that have some good suggestions for those who find their knuckles are indeed quite pale from hanging on to their sobriety by their fingernails.